20 research outputs found
Dynamics of neural cryptography
Synchronization of neural networks has been used for novel public channel
protocols in cryptography. In the case of tree parity machines the dynamics of
both bidirectional synchronization and unidirectional learning is driven by
attractive and repulsive stochastic forces. Thus it can be described well by a
random walk model for the overlap between participating neural networks. For
that purpose transition probabilities and scaling laws for the step sizes are
derived analytically. Both these calculations as well as numerical simulations
show that bidirectional interaction leads to full synchronization on average.
In contrast, successful learning is only possible by means of fluctuations.
Consequently, synchronization is much faster than learning, which is essential
for the security of the neural key-exchange protocol. However, this qualitative
difference between bidirectional and unidirectional interaction vanishes if
tree parity machines with more than three hidden units are used, so that those
neural networks are not suitable for neural cryptography. In addition, the
effective number of keys which can be generated by the neural key-exchange
protocol is calculated using the entropy of the weight distribution. As this
quantity increases exponentially with the system size, brute-force attacks on
neural cryptography can easily be made unfeasible.Comment: 9 pages, 15 figures; typos correcte
Synchronization of random walks with reflecting boundaries
Reflecting boundary conditions cause two one-dimensional random walks to
synchronize if a common direction is chosen in each step. The mean
synchronization time and its standard deviation are calculated analytically.
Both quantities are found to increase proportional to the square of the system
size. Additionally, the probability of synchronization in a given step is
analyzed, which converges to a geometric distribution for long synchronization
times. From this asymptotic behavior the number of steps required to
synchronize an ensemble of independent random walk pairs is deduced. Here the
synchronization time increases with the logarithm of the ensemble size. The
results of this model are compared to those observed in neural synchronization.Comment: 10 pages, 7 figures; introduction changed, typos correcte
Genetic attack on neural cryptography
Different scaling properties for the complexity of bidirectional
synchronization and unidirectional learning are essential for the security of
neural cryptography. Incrementing the synaptic depth of the networks increases
the synchronization time only polynomially, but the success of the geometric
attack is reduced exponentially and it clearly fails in the limit of infinite
synaptic depth. This method is improved by adding a genetic algorithm, which
selects the fittest neural networks. The probability of a successful genetic
attack is calculated for different model parameters using numerical
simulations. The results show that scaling laws observed in the case of other
attacks hold for the improved algorithm, too. The number of networks needed for
an effective attack grows exponentially with increasing synaptic depth. In
addition, finite-size effects caused by Hebbian and anti-Hebbian learning are
analyzed. These learning rules converge to the random walk rule if the synaptic
depth is small compared to the square root of the system size.Comment: 8 pages, 12 figures; section 5 amended, typos correcte
Successful attack on permutation-parity-machine-based neural cryptography
An algorithm is presented which implements a probabilistic attack on the
key-exchange protocol based on permutation parity machines. Instead of
imitating the synchronization of the communicating partners, the strategy
consists of a Monte Carlo method to sample the space of possible weights during
inner rounds and an analytic approach to convey the extracted information from
one outer round to the next one. The results show that the protocol under
attack fails to synchronize faster than an eavesdropper using this algorithm.Comment: 4 pages, 2 figures; abstract changed, note about chaos cryptography
added, typos correcte
Efficient statistical inference for stochastic reaction processes
We address the problem of estimating unknown model parameters and state
variables in stochastic reaction processes when only sparse and noisy
measurements are available. Using an asymptotic system size expansion for the
backward equation we derive an efficient approximation for this problem. We
demonstrate the validity of our approach on model systems and generalize our
method to the case when some state variables are not observed.Comment: 4 pages, 2 figures, 2 tables; typos corrected, remark about Kalman
smoother adde
Unbiased Bayesian inference for population Markov jump processes via random truncations
We consider continuous time Markovian processes where populations of
individual agents interact stochastically according to kinetic rules. Despite
the increasing prominence of such models in fields ranging from biology to
smart cities, Bayesian inference for such systems remains challenging, as these
are continuous time, discrete state systems with potentially infinite
state-space. Here we propose a novel efficient algorithm for joint state /
parameter posterior sampling in population Markov Jump processes. We introduce
a class of pseudo-marginal sampling algorithms based on a random truncation
method which enables a principled treatment of infinite state spaces. Extensive
evaluation on a number of benchmark models shows that this approach achieves
considerable savings compared to state of the art methods, retaining accuracy
and fast convergence. We also present results on a synthetic biology data set
showing the potential for practical usefulness of our work
Cox process representation and inference for stochastic reaction-diffusion processes
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling
Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
Stochastic fluctuations of molecule numbers are ubiquitous in biological
systems. Important examples include gene expression and enzymatic processes in
living cells. Such systems are typically modelled as chemical reaction networks
whose dynamics are governed by the Chemical Master Equation. Despite its simple
structure, no analytic solutions to the Chemical Master Equation are known for
most systems. Moreover, stochastic simulations are computationally expensive,
making systematic analysis and statistical inference a challenging task.
Consequently, significant effort has been spent in recent decades on the
development of efficient approximation and inference methods. This article
gives an introduction to basic modelling concepts as well as an overview of
state of the art methods. First, we motivate and introduce deterministic and
stochastic methods for modelling chemical networks, and give an overview of
simulation and exact solution methods. Next, we discuss several approximation
methods, including the chemical Langevin equation, the system size expansion,
moment closure approximations, time-scale separation approximations and hybrid
methods. We discuss their various properties and review recent advances and
remaining challenges for these methods. We present a comparison of several of
these methods by means of a numerical case study and highlight some of their
respective advantages and disadvantages. Finally, we discuss the problem of
inference from experimental data in the Bayesian framework and review recent
methods developed the literature. In summary, this review gives a
self-contained introduction to modelling, approximations and inference methods
for stochastic chemical kinetics.Comment: 73 pages, 12 figures in J. Phys. A: Math. Theor. (2016